Ludwig Staiger

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This paper links the concepts of Kolmogorov complexity (in complexity theory) and Hausdorff dimension (in fractal geometry) for a class of recursive (computable) ω -languages. It is shown that the complexity of an infinite string contained in a Σ 2 -definable set of strings is upper bounded by the Hausdorff dimension of this set and that this upper bound is(More)
If x = x1x2 · · ·xn · · · is a random sequence, then the sequence y = 0x10x2 · · · 0xn · · · is clearly not random; however, y seems to be “about half random”. Staiger [14, 15] and Tadaki [16] have studied the degree of randomness of sequences or reals by measuring their “degree of compression”. This line of study leads to various definitions of partial(More)
Lempel and Ziv (1976) proposed a computable string production-complexity. In this paper, our emphasis is on providing the rigorous development, where possible, for the theoretical aspects of a more recent and contrasting measure of string complexity. We derive expressions for complexity bounds subject to certain constraints. We derive an analytic(More)
In this paper we investigate several questions related to syntactic congruences and to minimal automata associated with ω-languages. In particular we investigate relationships between the so-called simple (because it is a simple translation from the usual definition in the case of finitary languages) syntactic congruence and its infinitary refinement (the(More)
In this paper we demonstrate that among all subspaces of GF(q) ! convolutional codes are best suited for error control purposes. To this end we regard several deening properties of convolutional codes and study the classes of subspaces deened by each of those properties alone. It turns out that these superclasses of the class of convolutional codes either(More)